Local Measures in Odd de Sitter

Abstract

We show that massless theories in odd-dimensional de Sitter space have very simple measures---the modulus squared of the late-time wavefunctional---at tree level. They are local functionals; in particular, all wavefunction coefficients vanish at separated positions. All the usual singularities of nonlocal wavefunctions in even dimensions only affect the phase in the odd dimensional case. Hence a closed formula can be written for any number of points. We focus on three examples: the non-linear sigma model, Yang-Mills theory and General Relativity, from dimensions three to seven.